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An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem

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  • Daniel Huppmann
  • Sauleh Siddiqui

Abstract

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity.

Suggested Citation

  • Daniel Huppmann & Sauleh Siddiqui, 2015. "An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem," Discussion Papers of DIW Berlin 1475, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp1475
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    More about this item

    Keywords

    binary Nash game; non-cooperative equilibrium; compensation; incentive compatibility; electricity market; power market; uplift payments;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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